Australian police have arrested a man over the death of an Israeli student who was killed while walking home late at night this week in Melbourne.

Aiia Maasarwe died on Wednesday shortly after she got off a tram in the Melbourne suburb of Bundoora.

A 20-year-old was taken into custody for questioning on Friday morning in the neighbouring suburb of Greensborough, a police statement said.

Police did not say if any charges have been filed.

Floral tributes are left at the scene (AP)

The 21-year-old victim was studying at La Trobe University in Melbourne as an exchange student from Shanghai University in China.

Police have not detailed the attack on Ms Maasarwe, which they assume was random and opportunistic.

Prime Minister Scott Morrison revealed that she had been raped before her body was found behind a hedge not far from the tram stop.

“I just want to begin by saying how devastated I am by the despicable, tragic and violent killing and rape of Aiia Maasarwe,” Mr Morrison told reporters in Fiji.

“Every woman in Australia — every person in Australia — should be able to travel home in safety. I can’t begin to think of what I could say to her family,” he added.

The woman was speaking to her sister by phone when the incident took place (AP)

Her uncle, Abed Kittani, told the Australian Broadcasting Corp that Ms Maasarve was speaking by phone to a younger sister when she was attacked.

“She heard the cars passing by and she was helpless, she couldn’t do anything,” Mr Kittani said of the sister. The sister sent messages, but there was no response.

“Instead of coming home with a diploma, she is coming back in a coffin,” Mr Kittani said.

Another uncle, Rame Maasarwe, said: “We cannot believe that something like this happened in Australia, we think it’s very safe there.”

On Friday, her father Saeed Maasarve stopped by a floral memorial to his daughter at La Trobe University. He travelled to Melbourne to bring her body home.

The Melbourne community organised a vigil outside Victoria state parliament. A tram carrying only flowers will depart from there following the route of her final journey later on Friday.

“Tonight, on the steps of parliament, Victorians will gather to remember Aiia Maasarwe. Positive. Fun. ‘The kindest girl.’ A 21-year-old just making her way in the world, with her whole life ahead of her. A student on her way home after a comedy show with friends,” Victorian premier Daniel Andrews tweeted.